This paper proposes a model in which business cycles are empirically characterized by a dynamic factor with regime switches. The approach captures both the idea of business cycles as comovements in several macroeconomic variables and the asymmetric nature of business cycle phases. The optimally inferred dates of business cycle turning points display a strong correlation with the NBER dating of business cycles and the extracted dynamic factor is remarkably similar to the Department of Commerce coincident indicator. In particular, the results highlight the importance of nonlinearities in business cycles.
The model provides a more rigorous and timely approach for dating business cycle turning points than traditional methods. In particular, our approach is based on a probabilistic framework that can be used in real time to assess the state of the economy and that can be replicated consistently at any time.
The results suggest that a very satisfactory representation of the sample data is obtained by modeling business cycles as the common element underlying a set of coincident variables subject to sporadic regime shifts. The proposed framework is also a useful tool for ex-ante prediction of business cycle turning points. Investigation using both revised data and
information available to agents in real time indicates that the extracted coincident index and estimated probabilities perform very well in their ability to characterize these turning points.
In the future, it might be worthwhile to investigate whether extending the approach in this paper to include leading macroeconomic variables might yield a leading indicator that could be successfully used to forecast turning points. Also, including additional states in the Markov stochastic process might improve the performance of the model. For example, Burns and Mitchell (1946) conceive business cycles as composed of four distinct periods: prosperity, crisis, depression and revivals. It might be interesting to investigate this notion using the framework studied in this paper.
In closing, let us address the relationship of this paper to the contemporaneous and independent work of Kim and Yoo (1995). Although the Kim-Yoo approach is similar to ours, there are important differences, related to choice of sample period, model specification, and the variables used. As regards sample period, the Kim-Yoo sample starts in 1960, which excludes two recessions compared to our sample data. Thus, our estimation uses information obtained from 8 recessions, while theirs uses information from 6 recessions. As regards model specification and the variables used, Kim and Yoo use the ENAP employment variable, which according to Stock and Watson (1991) requires extra lags in its equation to avoid model misspecification. This results in a mixed coincident/lagging index specification, which is unfortunate given that the objective is to construct a coincident index model. As was discussed in Section 4, we obtain a better-specified version of the switching dynamic factor model by using the employment series NACE instead of ENAP.
The upshot is simply that, because of differences in sample period, model specification, and the variables used, the Kim-Yoo coincident indicator behaves very differently from ours. The Kim-Yoo coincident indicator is highly correlated with Stock and Watson's (the correlation
between the two is greater than 0.99). Hence, both the Stock-Watson and Kim-Yoo coincident indexes fail to indicate the slow recovery following the last recession. This feature follows from the fact that their indexes are more correlated with changes in Industrial Production than with other variables, in particular for the subperiod around the 1990 recession. As discussed in the empirical section of our paper, Industrial Production shows a steep upturn near the trough of the 1990 recession. Although our index is highly correlated with Industrial Production as well, it captures the sluggish recovery because it is also highly correlated with variables that grew very slowly following the last recession, such as real personal income. Our conclusions about the last recession and the period that followed it are confirmed by an out-of-sample exercise using unrevised data, which Kim and Yoo did not perform.
Author’s Affiliation:
Marcelle Chauvet
Department of Economics
University of California, Riverside U.S.A.
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Figure 1 - Probability of Recession at t Using Information up to t, Prob(St=2|It) from Model 1, and Ex-Post NBER-Dated Recessions.
0.0 0.2 0.4 0.6 0.8 1.0
55 60 65 70 75 80 85 90
Figure 2 - Probability of Recession at t Using Full Sample Information: Prob(St=2|IT) from Model 1, and Ex-Post NBER-Dated Recessions.
0.0 0.2 0.4 0.6 0.8 1.0
55 60 65 70 75 80 85 90
Figure 3 - Probability of Recession at t Using Information up to t, Prob(St=2|It) from Model 2, and Ex-Post NBER-Dated Recessions.
0.0 0.2 0.4 0.6 0.8 1.0
55 60 65 70 75 80 85 90
Figure 4 - Probability of Recession at t Using Full Sample Information: Prob(St=2|IT) from Model 2, and Ex-Post NBER-Dated Recessions.
0.0 0.2 0.4 0.6 0.8 1.0
55 60 65 70 75 80 85 90
Figure 5 - Probability of Recession at t Using Full Sample Information: Prob(St=2|IT) from Hamilton’s Univariate Model Fitted to Monthly IP Growth Rates, and Ex-Post NBER-Dated Recessions.
0.0 0.2 0.4 0.6 0.8 1.0
55 60 65 70 75 80 85 90
Figure 6 - Growth Rates of the Switching Factor Index and NBER-Dated Recessions, Model 1.
-4 -2 0 2 4 6
55 60 65 70 75 80 85 90
Figure 7 - Growth Rates of the Switching Factor Index and NBER-Dated Recessions, Model 2.
-4 -2 0 2 4 6
55 60 65 70 75 80 85 90
Figure 8 - Switching Factor Index (___) and Department of Commerce Coincident Indicator (---), Model 1.
40 60 80 100 120 140
55 60 65 70 75 80 85 90
Figure 9 - Switching Factor Index (___) and Department of Commerce Coincident Indicator (---), Model 2.
40 60 80 100 120 140
55 60 65 70 75 80 85 90
Figure 10 - Stock-Watson Coincident Index (___) and Department of Commerce Coincident Indicator (---), Monthly Data.
40 60 80 100 120 140
55 60 65 70 75 80 85 90
Figure 11 - Out-of-Sample Filtered Probability of Recession, Prob(St=2|It), from Model 1; Revised Data (lower), and Department of Commerce Coincident Index (upper): 1990.01 to 1993.01.
0.0 0.2 0.4 0.6 0.8 1.0
122 124 126 128 130 132 134
90:1 90:3 91:1 91:3 92:1 92:3 93:1
Figure 12 - Out-of-Sample Filtered Probability of Recession, Prob(St=2|It), from Model 2; Revised Data: 1990.01 to 1993.03.
0.0 0.2 0.4 0.6 0.8 1.0
90:01 90:07 91:01 91:07 92:01 92:07 93:01
Figure 13 - Out-of-Sample Filtered Probability of Recession, Prob(St=2|It), from Model 2; Real Time Data: 1990.01 to 1993.03.
0.0 0.2 0.4 0.6 0.8 1.0
90:01 90:07 91:01 91:07 92:01 92:07 93:01
Figure 14 - Out-of-Sample One-Step Ahead Probability of Recession, Prob(St+1=2|It), from Model 2;
Real Time Data: 1990.01 to 1993.03.
0.0 0.2 0.4 0.6 0.8 1.0
90:01 90:07 91:01 91:07 92:01 92:07 93:01
Table 1
Maximum Likelihood Estimates - Model 1 Quarterly Data: 1952.2-1993.1
λpincome 0.456 p11 0.913
(.047) (.035)
λemploym 0.312 p22 0.754
(.028) (.093)
_____________________________________________________________
LogL(θ) -670.835
LR 28.92
_____________________________________________________________
Asymptotic standard errors in parentheses correspond to the diagonal elements of the inverse hessian obtained through numerical calculation. LR is the likelihood ratio test for the number of states. The variables used are: MTS, PLITP, ENAP and GDP, and the recession and expansion means are respectively µ2 = α2/(1- φ1- φ2) = -0.76 and µ1 = (α1+α2 )/(1- φ1 - φ2) = 2.29.
Table 2
Maximum Likelihood Estimates - Model 2 Monthly Data: 1952.04-1993.03 ∆Yit = λi∆Ft + ∆vit
σ2εpincome 0.156 demploym -0.171
(.013) (.052)
Asymptotic standard errors in parentheses correspond to the diagonal elements of the inverse hessian obtained through numerical calculation. LR is the likelihood ratio test for the number of states. The variables used are: MTS, PLITP, NACE and IP. The recession and expansion means are µ 2=α2/(1- φ1 ) = -1.05 and µ1=(α1 + α2 )/(1- φ1) =1.19. The log likelihood for a second-order autoregressive specification for both the factor and the disturbances is LogL(θ) = -1769. 59.
Table 3
Dating of U.S. Business Cycle Turning Points:
NBER, BEA and Smoothed Probabilities of Recession Models 1 and 2
_________________________________________________________________________________________________
Dates
NBER Dates
BEA Official Dates
Factor Model 1(*) Dates Factor Model 2
Peak Trough Peak Trough Peak Trough Peak Trough
_________________________________________________________________________________________________
1953:07 1954:05 1953:06 1954:08 1953:II 1954:II 1953:06 1954:05 1957:08 1958:04 1957:02 1958:04 1957:I 1958:II 1957:04 1958:04 1960:04 1961:02 1960:01 1961:02 1960:II 1960:IV 1960:02 1960:12 1969:12 1970:11 1969:10 1970:11 1969:IV 1970:IV 1969:12 1970:10 1973:11 1975:03 1973:11 1975:03 1974:I 1975:I 1973:12 1975:03 1980:01 1980:07 1980:01 1980:07 1979:IV 1980:II 1980:02 1980:06 1981:07 1982:11 1981:07 1982:12 1981:II 1982:IV 1981:08 1982:11 1990:07 1991:03 1990:06 1992:01 1990:II 1992:I 1990:06 1991:03
QPSNBER=0.1230 QPSNBER=0.0645 QPSBEA=0.0976 QPSBEA=0.0927
_________________________________________________________________________________________________
(*) Denotes quarterly dating.
The economy is assumed to be in a recession if P(St=2|ΙT) > 0.5.
Table 4
Statistics for the Extracted Coincident Factor Index (SFC) and the Department of Commerce Coincident Index (CCI,):
Quarterly and Monthly Data - Models 1 and 2
_____________________________________________________________________________________________
Model 1 Model 2
Growth Rates Level Growth Rates Level
Statistics CCI SFC CCI SFC CCI SFC CCI SFC
_____________________________________________________________________________________________
Mean 0.631 1.449 86.187 86.195 0.210 0.741 86.347 86.180 Stand Dev. 1.863 1.661 27.854 27.760 0.875 1.203 27.858 27.827
Corr.(SFC,CCI) -- 0.963 -- 0.998 -- 0.941 -- 0.984
_____________________________________________________________________________________________
Table 5
Evaluation of Turning Point Forecasts of the Filtered Probabilities of Recession: Revised and Real Time Data
________________________________________________________________________________
Revised Data Real Time Data Model 1 Model 2 Model 2 ________________________________________________________________________________
In-Sample QPSNBER 0.119 0.122
-QPSBEA 0.101 0.192
-________________________________________________________________________________
Out-of-Sample QPSNBER 0.289 0.113 0.164
QPSBEA 0.078 0.464 0.438
Corr. with
NBER 0.815 0.775 0.588
Corr. with BEA 0.897 0.595 0.523
________________________________________________________________________________
The criterion adopted to determine if the economy is in a recession is whether the filtered probability of recession is greater than 0.5, P(St=2|It) > 0.5. The Quadratic Probability Score is: QPS
=2
T {p[S = 2|I ] - N }t t t 2 t 1
T
=∑ , where Nt is a 0/1 dummy corresponding to the BEA or NBER dating